Neil Tennant presents an original logical system with unusual philosophical, proof-theoretic, metalogical, computational, and revision-theoretic virtues. Core Logic, which lies deep inside Classical Logic, best formalizes rigorous mathematical reasoning. It captures constructive relevant reasoning. And the classical extension of Core Logic handles non-constructive reasoning. These core systems fix all the mistakes that make standard systems harbor counterintuitive irrelevancies. Conclusions reached by means of core proof are relevant to the premises used. These are the first systems that ensure both relevance and adequacy for the formalization of all mathematical and scientific reasoning. They are also the first systems to ensure that one can make deductive progress with potential logical strengthening by chaining proofs together: one will prove, if not the conclusion sought, then (even better!) the inconsistency of one's accumulated premises. So Core Logic provides transitivity of deduction with potential epistemic gain. Because of its clarity about the true internal structure of proofs, Core Logic affords advantages also for the automation of deduction and our appreciation of the paradoxes.

"Due to the author's clear and approachable style this book may be interesting to a large circle of logicians, mathematicians and philosophers." - Branislav Boricic

"Although the author's approach is purely logical and philosophical, rather than mathematical, it seems likely that the book would be extremely interesting to mathematicians specializing in logic and the foundations of mathematics. Due to the author's clear and approachable style this book may be interesting to a large circle of logicians, mathematicians and philosophers. Students with a basic understanding of classical, intuitionistic and relevant logic principles will find this book an invaluable introduction to an area of central importance in logic, philosophy, computer science and, generally, methodology and philosophy of science." - Branislav Boricic, mathSciNet